Methods and tools are known, for example from U.S. Pat. No. 4,468,623, U.S. Pat. No. 6,600,321, U.S. Pat. No. 6,714,014 or U.S. Pat. No. 6,809,521 using current injection measurements in order to obtain micro-electric images of a borehole wall, the borehole penetrating geological formations.
When the borehole is filled with a conductive mud, e.g. a water-base mud, such methods and tools normally operate at low frequencies, e.g. below 20 kHz. In conductive mud, the interpretation of the measured current is easily related to the local resistivity of the borehole wall.
When the borehole is filled with a non-conductive or resistive mud, e.g. an oil-base mud, such methods and tools operate at high frequencies, e.g. above around 100 kHz. In a first approximation, in non-conductive or resistive mud the survey current is controlled by the impedance of the mud and the impedance of the formation, combined in series. In this approximation, the impedance between the geological formation and a current return of the tool is neglected. The impedance of the mud is the impedance between a survey current sensor and the geological formation. If the mud impedance is significantly greater than the formation impedance then the measurement is insensitive to the formation impedance. In this case a higher frequency is needed to reduce the mud impedance, by the capacitive effect, so that the formation impedance can be measured.
At high frequencies, in the resistivity range between about 0.1 and 10 Ωm, the phase of the survey current is the most sensitive parameter enabling characterizing the resistivity of the geological formation. At high frequencies, in the resistivity range between about 100 and 1000 Ωm, the magnitude of the survey current is the most sensitive parameter enabling characterizing the resistivity of the geological formation.
FIGS. 1 and 2 show curves representing the magnitude Abs(ZM) and phase φ(ZM) of the impedance measured for various geological formations resistivities at different frequencies. The impedance is measured with a resistive oil base mud. The value of the geological formation resistivity, namely 1 Ωm, 10 Ωm, 100 Ωm, 1000 Ωm, 10000 Ωm is indicated on each curve. The measurements have been made for three frequencies, namely 10 kHz, 1 MHz and 100 MHz. The magnitude Abs(ZM) axis is based on a logarithmic scale while the phase φ(ZM) axis is based on a linear scale.
FIG. 1 shows various curves for various standoffs so. The standoff is the distance between the survey current sensor and the borehole wall. In FIG. 1, curves for three different standoffs so are illustrated, namely 1 mm (dotted line with reversed triangle), 3 mm (plain line with circle) and 10 mm (dotted line with triangle).
FIG. 2 shows various curves for various geological formation permittivity ε. In FIG. 2, curves for three different permittivity ε are illustrated, namely 0.5εf (dotted line with reversed triangle), εf (plain line with circle) and 2εf (dotted line with triangle), where εf is a typical formation permittivity determined, for example, from laboratory measurements.
FIGS. 1 and 2 illustrate that the measurement behaves differently for low frequencies in the order of 10 kHz, high frequencies in the order of 1 MHz, and very high frequencies in the order of 100 MHz. It is to be noticed that a wrap-around effect for the phase occurs for high and very high frequencies. Thus, it is not possible to use the phase directly as a resistivity measurement at high and very high frequencies. Further, the sensitivity of the measurements is severely decreased for low and very high formation resistivities when using the magnitude as a resistivity measurement. In addition, FIG. 1 illustrates how the standoff influences the phase measurements, in particular below 10000 Ωm, and the magnitude measurements, in particular below 1000 Ωm. Finally, FIG. 2 illustrates how the permittivity influences the phase measurements and the magnitude measurements. Thus, a change of standoff and/or permittivity strongly influences the measurements because both the magnitude and the phase are changed for same value of the geological formations resistivity.
In the prior art, either the magnitude of the survey current or the real part of the inverse of the survey current are used in the determination of the resistivity of the geological formations. Consequently, with a borehole filled with a non-conductive/resistive mud, a change of standoff and/or permittivity significantly influences the determination of the resistivity of the geological formations. Therefore, the methods and tools according to the hereinbefore mentioned prior art may have an insufficient accuracy.